Phase Diagrams

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Phase Diagrams

• Chapter 10
• Callister, 2006

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Outline of the Lecture

• 1) Definitions
• 2) Equilibrium Phase Diagrams
• ----Binary Isomorphous Systems
• ----Binary Eutectic Systems
• 3) The Iron-Carbon System

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Why do we study phase diagrams?

• There is a strong correlation between
  microstructure and mechanical properties and
  development of microstructure can be understood
  from the phase diagrams. Moreover phase diagrams
  can be used to obtain information about melting,
  casting, crystallization, etc.

SEM micrograph of plain C steel with 0.44 wt C
(3000X).
Preeutectoid ferrite
Pearlite (dark layer is ferrite, Light layer is
cementite)
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• Major terms used in this lecture
• Component pure metals or elements in the
  composition of an alloy.
• Solute and solvent (Week 4)
• System specific body of material or series of
  alloys consisting the same components (
  iron-carbon system)
• Solubility Limit The maximum amount of solute
  that may dissolve in solvent to form a solid
  solution. Addition of solute beyond the
  solubility limit causes the formation of another
  phase.
• Phase is a homogeneous portion of a
  system that has uniform physical and chemical
  characteristics. Gas, liquid and solid phase.

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Sugar and Water
how many phases are there?
(a single phase)
(two-phase system)
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• For example if a substance can exist in two or
  more polymorphic forms (BBC and FCC) each of
  these structures is a separate phase because
  their physical properties are different.
• A single phase system is called homogeneous
  system.
• System of two or more phases is called a mixture
  or heterogeneous system. Therefore most of the
  metallic alloys,ceramics, polymeric and composite
  systems are heterogeneous.
• Microstructure is subject to direct microscopic
  observation using microscopic techniques. The
  number of phases, their proportions, and the way
  they are distributed or arranged can be
  characterized by the same techniques.
• Phase Equilibria A system is said to be at
  equilibrium when the free energy, which is the
  internal energy and randomness of the atoms, is
  at minimum under some specified combination of
  temperature, pressure and composition.
• In other words, at equilibrium the
  characteristics of the system do not change with
  time but persist indefinetely. This system is
  also called stable.

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• The diagrams showing the solubility (solubility
  charts) do not give information about the time
  necessary to achieve the equilibrium. It is often
  the case that a state of equilibrium is never
  completely achieved because the rate of approach
  to equilibrium is slow. Such a system is said to
  be nonequilibrium or metastable state.
• Therefore not only the understanding of
  equilibrium states are important but also the
  rate at which they are established, and the
  factors affecting this rate.
• Equilibrium Phase Diagrams
• Phase diagram is also called equilibrium or
  constitutional diagram.
• These diagrams defines the relationship between
  the temperature and compositions or quantities of
  phases at EQM. External pressure could also be
  another parameter affecting the phase
  distribution but it remains constant at 1 atm in
  most of the applications.

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• Isomorphous Binary Systems
• Binary systems are composed of two components and
  they are isomorphous since there is a complete
  solubility of liquids and solids.
• Example Cu-Ni

Liquid forms of Cu and Ni (L)
m.p. of Ni
Mixture of solid and Liquid phases (aL)
Substitutional Solid solution of Cu and Ni
(a) Structure is FCC.
Below 10850C, Cu and Ni are soluble in each
other at all compositions.
m.p. of Cu
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• The lower case Greek letters (a, ß, ?, etc.)
  indicate solid solutions.
• The line separating L and aL phases is liquidus
  line.
• The line separating a and aL phases is called
  solidus line.
• Take 50 wt Ni and 50 wt Cu alloy melting
  begins around 12800C and the amount of liquid
  increases with temperature until about 13200C and
  above this temperature the alloy is completely
  liquid.
• From the phase diagrams we can learn the
  followings
• Phases that are present
• Composition of the phases
• Fractions of the phases
• Example 60 wt Ni-40 wt Cu alloy at 11000C
  (pt A). There is a single phase, which solid (a).
• Pt B (35 wt Ni-65 wt Cu) is the mixture of
  solid and liquid on the same plot.

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• Determination of the composition in a single
  phase is trivial. But in two phase, the
  calculation is as follows
• A tie line (horizontal line passing from the
  temperature) is constructed.
• The intersections of tie line and phase
  boundaries are noted.
• Each respective composition is read from the
  composition axis.
• For example point B in Figure 10.2a
• 35 wt Ni-65 wt Cu at 12500C aL

CL (Composition of the liquid phase)
Ca (Composition of the solid phase)
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• Phase Amounts For a single phase it is 100 of
  solid or liquid.
• For two phase systems Lever rule
• Draw the tie line
• Locate the overall composition of the alloy on
  the line
• The fraction of one phase is computed by taking
  the length of the line from the overall
  composition to the phase boundary of the other
  phase.
• Do the same thing for the other phase.
• Multiply each fraction by 100.

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• Similary for solid phase

For multiphase alloys relative phase amounts can
be reported in volume fraction rather than mass
fraction. For an alloy with a and ß phases, the
volume fraction of the a phase, Va
volume of a
volume of ß
Conversion from mass fraction to volume fraction
can be accomplished using the equations
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• Mechanical properties of solid isomorphous alloys
  can be improved by solid solution strengthening
  or by the addition of other components.

Tensile strength and elongation are two opposite
mechanical properties of the material This is
why one has the maximum value while the other has
the minimum.
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• Binary Eutectic Systems Cu and Ag system

Three single phase a FCC structure ß FCC
structure
max. solubility of Cu in Ag (8.8 wt)
Max. Solubility of Ag in Cu 8 wt Ag at 7790C
maximum solubility line, which is also solidus.
This line shows the minimum temperature for the
liquid phase existence.
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Three two phase regions.
Composition and the fraction of the phases can be
determined by lever rule.
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• As Ag is added to Cu, the melting point of alloy
  decreases along the liquidus line, which is the
  same for Ag. The minimum melting point is at
  point E (invariant point), which is defined CE
  (71.9 wt Ag) and TE (7790C).
• There is an imp. Rxn (eutectic reaction) for the
  alloy with a composition of CE as the temperature
  decreases

Eutecticeasily melted
Eutectic isotherm
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• Notice that in the eutectic phase diagram a and ß
  phases exist over the composition ranges near the
  concentration extremities, this is why they are
  also called terminal solid solutions. For other
  alloy systems, there may be intermediate solid
  solutions, such as Cu-Zn (brass) system.

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• For some alloy systems, discrete intermediate
  compounds rather than solid solutions may be
  observed in phase diagrams. For example Mg-Pb
  system. These are called intermetallic compounds.
  The compound Mg2Pb is shown as a vertical line on
  the diagram rather than a phase region since it
  exists precisely at the composition defined.

This diagram can be thought as two eutectic phase
diagrams of Mg-Mg2Pb and Mg2Pb-Pb systems.
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• Eutectoid and Peritectic Reactions
• Consider Cu-Zn system.

Eutectoid reaction 5600C and 74 wt Zn -26 wt
Cu
Notice that one solid phase forms two other solid
phases upon cooling. This is also seen in Fe-C
systems.
Peritectic reaction 5980C and 78.6 wt Zn- 21.4
wt Cu
Notice that a solid transforms into another
solid and a liquid.
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• Phase transformations can be classified according
  to whether or not there is any change in
  composition. Those which have no changes in
  composition are called as congruent
  transformations. The opposite is incongruent
  transformation. Allotropic transformations are
  congruent as well as melting pure metals.
  Eutectic, eutectoid or melting alloy systems are
  incongruent transformations.
• Phase diagrams of the metallic systems composed
  of more than two metal (or component) are very
  complex. There is a need for 3-D diagram to
  analyze such systems.

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Iron-Carbon System

• This is the most important system in
  manufacturing since primary structural materials
  are essentially Fe-C alloys, such as, steel and
  cast iron.
• The Iron-Iron Carbide System -Phase Diagram

Pure Fe at room T is stable and it has a BCC
structure. This form of the Fe is called ferrite
or a Fe. As T increases, ferrite experiences a
polymorphic transformation to FCC austenite
(?-Fe) at 9120C. At 15380C FCC austenite
transforms back to BCC d ferrite.
This system is Fe rich
graphite
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• At 6.70 wt C composition, an intermediate
  compound, iron carbide (Fe3C) or cementite is
  formed. In practice all steels and cast irons
  have C content less than 6.70 wtC, which
  corresponds to 100 Fe3C.

relatively soft, can be made magnetic at 7680C
and has a density of 7.88 g/cm3. max. solubility
of C is 0.022 wt at 7270C.
max. solubility of C is 2.14 wt at 11470C.
This is nonmagnetic.
C is an interstitial impurity and can form solid
solutions with each of the iron
(ferrite, austenite, and d ferrite.
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• d-ferrite and a-ferrite are virtually the same
  except the temperatures over which they exist.
• Cementite forms when the solubilty limit of C is
  exceeded in a-ferrite below 7270C. Cementite is
  hard and brittle, which enhances the strength of
  the steel. Cementite is a metastable at RT. When
  it is heated to 650-7000C for several years, then
  it will transform in to a iron and carbon.
  Therefore cementite in the phase diagram is not
  compound at equilibrium, but since the rate of
  its transformation is very slow we can assume the
  compound to be stable in steel for instance.
• Eutectic reaction

at 4.30 wt Cand 11470C
Eutectoid reaction
7270C
These equations are extremely important in the
heat treatment of steels.
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• 
  Ferrous Alloys
• (Iron is the
  primary component)
• based on C
  content of the alloy

Cast Iron 2.14-6.70 wtC
Steel 0.008-2.14 wt C a and Fe3C
Iron lt0.008 wt C ferrite
Development of Microstructure in Iron-Carbon
alloys Microstructures of Fe-C alloys depend on
C content and heat treatment. Assume here that
cooling is very slow and equilibrium is
maintained continuously. For a phase of a
eutectic alloy cooling from the temperature range
of austenite
Pearlite properties b/w soft, ductile ferrite and
hard brittle cement.
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• The alternating a and Fe3C layers in pearlite
  causes the redistribution of C by diffusion as
  shown during phase transformation

Hypoeutectoid alloys Alloys with C content
between 0.022 and 0.76 wt are hypoeutectoid
alloys.
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proeutectoid ferrite
pearlite some pearlite grains look darker
because of the magnification used.
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• The fractions of the phases can be calculated
  using lever rule.

Fraction of pearlite
Fraction of proeutectoid ferrite
Fraction of total a and cementite is
determined by using tie line extending from 0.022
to 6.70 wt C
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• Hypereutectoid Alloys alloys with C content of
  b/w 0.76 - 2.14 wt cooled from austenite T
  range.

proeutectoid cementite
pearlite
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Things learned

• What is a phase diagram?
• Interpretation of the phase diagrams.
• Types of the phase diagrams.
• Phase diagram of Fe-C alloy system.
• Changes in the microstructure of Fe-C alloys
  during slow cooling.